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In this letter, we propose a Gaussian mixture model (GMM)-based channelestimator which is learned on imperfect training data, i.e., the training dataare solely comprised of noisy and sparsely allocated pilot observations. In apractical application, recent pilot observations at the base station (BS) canbe utilized for training. This is in sharp contrast to state-of-theart machinelearning (ML) techniques where a training dataset consisting of perfect channelstate information (CSI) samples is a prerequisite, which is generallyunaffordable. In particular, we propose an adapted training procedure forfitting the GMM which is a generative model that represents the distribution ofall potential channels associated with a specific BS cell. To this end, thenecessary modifications of the underlying expectation-maximization (EM)algorithm are derived. Numerical results show that the proposed estimatorperforms close to the case where perfect CSI is available for the training andexhibits a higher robustness against imperfections in the training data ascompared to state-of-the-art ML techniques.

Learning a Gaussian Mixture Model from Imperfect Training Data for Robust Channel Estimation